In order to determine how quickly two objects that do not differ greatly in mass will accelerate toward each other, you should consider the gravitational force of each, then apply Newton's Second Law to each mass and then add the magnitudes of their accelerations.
Note: Suppose that the gravitational force on object A causes it to accelerate in the direction of object B at 10 m/s(^2). Since object B is half as massive as object A, object B accelerates toward object A at 20 ms(^2), even though the gravitational force on B is of equal magnitude. These values represent the separate accelerations of the objects, but the two bodies are accelerating toward each other at a faster rate. Adding the magnitudes of the objects' individual accelerations gives a value of 30 m/s(^2), the rate at which the objects are accelerating toward each other. Object B is accelerating relative to object A at 30 m/s(^2), but it is accelerating relative to a stationary boundary A at only 20 m/s(^2).